Abstract We study the quantum Kagomé ice hardcore bosons, which correspond to the XY limit of the quantum spin ice Hamiltonian. We estimate the values of their zero-temperature thermodynamic quantities using the large- S expansion. We show that our semiclassical analysis is consistent with the finite temperature quantum Monte Carlo estimates.
Abstract We study the quantum Kagomé ice hardcore bosons, which correspond to the XY limit of the quantum spin ice Hamiltonian. We estimate the values of their zero-temperature thermodynamic quantities using the large- S expansion. We show that our semiclassical analysis is consistent with the finite temperature quantum Monte Carlo estimates.
We present a large-S study of a quantum spin ice Hamiltonian, introduced by Huang et al. [Phys. Rev. Lett. 112, 167203 (2014)], on the kagome lattice. This model involves a competition between the frustrating Ising term of classical kagome ice, a Zeeman magnetic field h, and a nearest-neighbor transverse spin-flip term ${S}_{i}^{x}{S}_{j}^{x}\ensuremath{-}{S}_{i}^{y}{S}_{j}^{y}$. Recent quantum Monte Carlo (QMC) simulations by Carrasquilla et al. [Nat. Commun. 6, 7421 (2015)], uncovered lobes of a disordered phase for large Ising interaction and $h\ensuremath{\ne}0$---a putative quantum spin liquid phase. Here, we examine the nature of this model using large-S expansion. We show that the ground state properties generally have the same trends with those observed in QMC simulations. In particular, the large-S ground state phase diagram captures the existence of the disordered lobes.
Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla et al., [Nat. Commun., 6, 7421 (2015)], we study the ground-state properties of this model on the triangular lattice. In the presence of a magnetic field h, the Hamiltonian possesses competing interactions between a Z2-invariant easy-axis ferromagnetic interaction ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$ and a frustrated Ising term Jz. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z2-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large h, an easy-axis canted ferromagnet (CFM) with broken Z2 symmetry for small h and dominant ${J}_{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}$, a ferrosolid phase with broken translational and Z2 symmetries for small h and dominant Jz, and two lobes with $m=\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}=\ifmmode\pm\else\textpm\fi{}1/6$ for small h and dominant Jz. We show that quantum fluctuations are suppressed in this model, hence the large-S expansion gives an accurate picture of the ground-state properties. When quantum fluctuations are introduced, we show that the ferrosolid state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for ${J}_{z}\ensuremath{\rightarrow}\ensuremath{\infty}$. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no Sz order. We present the trends of the ground-state energy and the magnetizations. We also present a detail analysis of the CFM.
Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla, et al., [Nature Communications 6, 7421 (2015)], we study the ground state properties of this model on the triangular lattice. In the presence of a magnetic field h, the Hamiltonian possesses competing interactions between a Z2-invariant easy-axis ferromagnetic interaction J±± and a frustrated Ising term Jz. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z2-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large h, an easy-axis canted ferromagnet (CFM) with broken Z2 symmetry for small h and dominant J±±, a {\it ferrosolid} phase with broken translational and Z2 symmetries for small h and dominant Jz, and two lobes with m=⟨Sz⟩=±1/6 for small h and dominant Jz. We show that quantum fluctuations are suppressed in this model, hence the large-S expansion gives an accurate picture of the ground state properties. When quantum fluctuations are introduced, we show that the {\it ferrosolid} state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for Jz→∞. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no Sz-order. We present the trends of the ground state energy and the magnetizations. We also present a detail analysis of the CFM.
Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla, et al., [Nature Communications 6, 7421 (2015)], we study the ground state properties of this model on the triangular lattice. In the presence of a magnetic field h, the Hamiltonian possesses competing interactions between a Z2-invariant easy-axis ferromagnetic interaction J±± and a frustrated Ising term Jz. As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z2-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large h, an easy-axis canted ferromagnet (CFM) with broken Z2 symmetry for small h and dominant J±±, a {\it ferrosolid} phase with broken translational and Z2 symmetries for small h and dominant Jz, and two lobes with m=⟨Sz⟩=±1/6 for small h and dominant Jz. We show that quantum fluctuations are suppressed in this model, hence the large-S expansion gives an accurate picture of the ground state properties. When quantum fluctuations are introduced, we show that the {\it ferrosolid} state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for Jz→∞. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no Sz-order. We present the trends of the ground state energy and the magnetizations. We also present a detail analysis of the CFM.
We derive an effective Z2 gauge theory to describe the quantum kagome ice (QKI) state that has been observed by Carrasquilla et al. [Nat. Commun. 6, 7421 (2015)] in Monte Carlo studies of the S=21 kagome XYZ model in a Zeeman field. The numerical results on QKI are consistent with, but do not confirm or rule out, the hypothesis that it is a Z2 spin liquid. Our effective theory allows us to explore this hypothesis and make a striking prediction for future numerical studies, namely, that symmetry-protected vison zero modes arise at lattice disclination defects, leading to a Curie defect term in the spin susceptibility, and a characteristic $({N}_{\mathrm{dis}}\ensuremath{-}1)ln2$ contribution to the entropy, where Ndis is the number of disclinations. Only the Z2 Ising symmetry is required to protect the vison zero modes. This is remarkable because a unitary Z2 symmetry cannot be responsible for symmetry-protected degeneracies of local degrees of freedom. We also discuss other signatures of symmetry fractionalization in the Z2 spin liquid, and phase transitions out of the Z2 spin liquid to nearby ordered phases.
We carry out an analytical study of quantum spin ice, a U(1) quantum spin liquid close to the classical spin ice solution for an effective spin 1/2 model with anisotropic exchange couplings Jzz, J± and Jz± on the pyrochlore lattice. Starting from the quantum rotor model introduced by Savary and Balents in Phys. Rev. Lett. 108, 037202 (2012), we retain the dynamics of both the spinons and gauge field sectors in our treatment. The spinons are described by a bosonic representation of quantum XY rotors while the dynamics of the gauge field is captured by a phenomenological Hamiltonian. By calculating the one-loop spinon self-energy, which is proportional to Jz±2, we determine the stability region of the U(1) quantum spin liquid phase in the J±/Jzz vs Jz±/Jzz zero temperature phase diagram. From these results, we estimate the location of the boundaries between the spin liquid phase and classical long-range ordered phases.